{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "数式処理group work-2(関数と微分)\n", "
\n", "
\n", "
\n", "file:/~/python/doing_math_with_python/symbolic_math/gw2_diff_ans.ipynb\n", "
\n", "cc by Shigeto R. Nishitani 2009-2021 \n", "
\n", "\n", ": ruby bin/pick_works_from_ans.rb gitignores/gw2_diff_ans.ipynb -1 '4 17 23' '13'\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "対数関数の狙いが先週の課題で明らかになったでしょうか.\n", "主な応用分野は制御系の計算で,その昔は大砲の着弾距離を計算するのが主な仕事でした.\n", "では,対数・指数でexpってのがありますが,\n", "なんであんな中途半端な数を使わにゃいかんニャロって思ったことないですか.\n", "それを導いてもらおうというのが今日の狙いです.\n", "\n", "# 問1: $2^x$のplot\n", "指数関数\n", "$$\n", "f(x; b=2) = b^x\n", "$$\n", "について考える.\n", "$f(x; b=2)$の表記は,$b$が助変数で,そのデフォルト値が2であることを意図している.\n", "1. 次の表を埋めよ.また,\n", "2. 関数$f(x; 2)$をプロットして確認せよ.\n", "\n", "| x | -1 | 0 | 1 | 2 | 3 |\n", "| ---|---|---|---|---|---|\n", "| f(x; 2)|" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5\n", "1\n", "2\n", "4\n", "8\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sympy import *\n", "def f(x, b=2):\n", " return b**x\n", "\n", "for i in range(5):\n", " print(f(i-1))\n", "\n", "%matplotlib inline\n", "x = symbols('x') \n", "p = plot(f(x),\n", " (x, -1, 3), ylim=[0,8],\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| x | -1 | 0 | 1 | 2 | 3 |\n", "| ---|---|---|---|---|---|\n", "| f(x)|0.5|1.0|2.0|4.0|8.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 問2: 平均変化率\n", "問1.の指数関数に対して,平均変化率\n", "$$\n", "m0(x; h) = \\frac{f(x+h)-f(x)}{x+h-x}\n", "$$\n", "を求める式を考える.\n", "\n", "1. x=0..2(x=0からx=2)の傾きを求めよ.\n", "2. それらの点の間を結ぶ直線の方程式を求めよ.\n", "3. また,元の関数と同時にプロットせよ.\n", "4. x=0..1(x=0からx=1)についても同様に求め,同時にプロットせよ.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from sympy import *\n", "def f(x, b=2):\n", " return b**x\n", "def m0(x0, h):\n", " return (f(x0+h)-f(x0))/(h)\n", "\n", "print(m0(0,1))\n", "x = symbols('x') \n", "p = plot(f(x), m0(0,2)*x+f(0), \n", " m0(0,1)*x+f(0), \n", " (x, -1, 3), ylim=[0,8],\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p[2].line_color = 'g'\n", "p.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 問3: 接線\n", "1. 問1.の関数に対して,x=0における接線の傾きを微分により求めよ.また問2.でx=0..0.1に対して求めた平均変化率と小数点以下5桁で比べよ.\n", " 1. なお浮動小数点数での表示は,`print(\"%10.5f\" % log(2))`が便利.\n", "2. 問1.の関数に対して,x=0における接線の方程式を求め,同時にプロットせよ.\n", "3. 問2.で求めた接線をx=0..0.1の平均変化率に対して求め, ~~1.~~ 2.で作成した関数および問1.の関数と同時プロットして比較せよ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "問3,4,5の解答例では問1,2の解答例と違って,テキストの表記に従っているので注意せよ." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2**x*log(2)\n", "log(2)\n", " 0.69315\n", " 0.71773\n" ] } ], "source": [ "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "f0 = 2**x\n", "df0 = diff(f0,x)\n", "print(df0)\n", "\n", "x0 = 0\n", "a = df0.subs({x:x0})\n", "print(a)\n", "print(\"%10.5f\" % log(2))\n", "print(\"%10.5f\" % m0(0, 0.1))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x⋅log(2) + 1\n" ] } ], "source": [ "f1 = a*(x-x0)+f0.subs({x:x0})\n", "pprint(f1)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from sympy.plotting import plot\n", "\n", "p = plot(f0,f1,\n", " m0(0,0.1)*x+f(0), \n", " (x, -1,3), ylim=[0,8],\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 問4: 関数とその一次導関数の同時プロット\n", "問1.の関数とその一次導関数を同時にプロットすると次のようになる.一次導関数の意味を言葉で述べよ." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2**x\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from sympy.plotting import plot\n", "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "f0 = 2**x\n", "print(f0)\n", "f1 = diff(f0,x)\n", "p = plot(f0,f1,\n", " (x, -1,3), ylim=[0,8],\n", " show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 問5: 一次導関数が恒等的にほぼ一致する$b$\n", "関数\n", "$$\n", "f(x) = b^x, \\, \\textrm{where} \\,2 < b < 3\n", "$$\n", "と,その一次導関数が恒等的にほぼ一致する$b$を,\n", "上のグラフの指数関数の底’2’を色々変えて小数点以下1桁で求めよ." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.7**x\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from sympy.plotting import plot\n", "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "f0 = 2.7**x\n", "print(f0)\n", "f1 = diff(f0,x)\n", "p = plot(f0,f1,\n", " (x, -1,3), ylim=[0,8],\n", " show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 問6: ネイピア数のオイラーによる定義\n", "問5で求めた数は自然対数の底e(ネイピア数)のオイラーによる定義である.\n", "1. ネイピア数の定義を,この導出にしたがって,言葉で述べよ.\n", "2. $f(x; b)=b^x$を問2.の平均変化率の定義に代入し変形することによって,\n", "$$\n", "m2(h; b) = \\frac{b^h-1}{h}\n", "$$\n", "としたときに,$b$がネイピア数であるならば$m2(h; b)$が$h \\rightarrow 0$で取るべき値はなんであるか.\n", "3. また,\n", "\n", "> plot(m2(h, 2),m2(h, exp(1)),m2(h, 3),(h, -1, 3))\n", "\n", "で結果を確かめよ. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 解答例\n", "ネイピア数は,指数関数に於いて,一次導関数がそれ自身の関数と一致する指数関数の底となる実数として定義できる.\n", "\n", "$f(x; b)=b^x$を平均変化率の式に入れると\n", "$$\n", "m1(x; h, b) = \\frac{b^{x+h}-b^x}{h}=b^x \\frac{b^h-1}{h}\n", "$$\n", "である.これを$h\\rightarrow 0$にとると\n", "$$\n", "\\lim_{h\\rightarrow 0}m1(x; h, b) = \n", "b^x \\lim_{h\\rightarrow 0}\\frac{b^h-1}{h}\n", "$$\n", "となる.これがその関数自身と等しくなるためには,\n", "$$\n", "\\lim_{h\\rightarrow 0}\\frac{b^h-1}{h} = 1\n", "$$\n", "である必要がある.\n", "\n", "これを変数が$h$,助変数が$b$の関数\n", "$$\n", "m2(h; b) = \\frac{b^h-1}{h}\n", "$$\n", "とみなして,b = 2, exp(1), 3をとってplotすると次の通りとなる.\n", "h=0に於いて,値が1となるのは,exp(1)であることが確認できる.\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from sympy import *\n", "def m2(h, b):\n", " return (b**h-1)/h\n", "\n", "h = symbols('h') \n", "p = plot(m2(h, 2), m2(h, exp(1)), \n", " m2(h, 3), \n", " (h, -1,3), ylim=[0,4],\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p[2].line_color = 'g'\n", "p.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この$m1(x; h, b)$には少し注意が必要.\n", "$m1(x, h; b)$として扱った方がいいかも.\n", "なぜならば,平均変化率を取るときには,\n", "$h$を助変数としていたが,最後のplotでは\n", "独立変数として導いている." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 問7: おまけ(時間が余ったらやってください)\n", "関数\n", "$$\n", "f_1(x) = \\frac{x}{x^2-2x+4}\n", "$$\n", "を考える.\n", "1. $f_1(x)$を積分した関数$f_0(x)$を求めよ.\n", "2. 関数$f_1(x)$の1次導関数$f_2(x)$を求め,3つの関数を同時にプロットせよ.\n", "3. この$f_0$関数の極小値,変曲点の$x$座標をグラフから求めよ.\n", "4. この$f_0$関数の増減表を作れ." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x/(x**2 - 2*x + 4)\n", "log(x**2 - 2*x + 4)/2 + sqrt(3)*atan(sqrt(3)*x/3 - sqrt(3)/3)/3\n", "(2*x - 2)/(2*(x**2 - 2*x + 4)) + 1/(3*((sqrt(3)*x/3 - sqrt(3)/3)**2 + 1))\n" ] } ], "source": [ "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "f1 = x/(x**2 -2*x + 4)\n", "print(f1)\n", "print(integrate(f1,x))\n", "f0 = integrate(f1,x)\n", "print(diff(f0,x))\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from sympy import *\n", "\n", "f2 = diff(f1,x)\n", "\n", "p = plot(f0,f1,f2, legend=True,show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p[2].line_color = 'g'\n", "\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "| $x$ |$\\cdots$| -2 |$\\cdots$| 0 |$\\cdots$| 2 |$\\cdots$|\n", "|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n", "| $f_0(x)$|$\\frown \\searrow$|.|$\\smile \\searrow$|min|$\\smile \\nearrow$|.|$\\frown \\nearrow$|\n", "| $f_1(x)=\\frac{df_0}{dx}$|-|-|-|0|+|+|+|\n", "| $f_2(x)=\\frac{d^2f_0}{dx^2}$|-|0|+|+|+|0|-|" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": false, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": { "height": "13px", "width": "253px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": true }, "vscode": { "interpreter": { "hash": "f3f87633aac09da3bda522f97956bee375b5501d1579e6458804e567301cb62a" } } }, "nbformat": 4, "nbformat_minor": 2 }